I don't think that will contribute to essentials, but luckily for you that is not for me to decide.

However, although I didn't really look into this, I think you may be able to do this yourself:

Using graphics (probably the easiest):
1. show a video. Look at the intro for an example, look at the battlescripts to use the right settings of all images. (If no interaction is needed, then why go through all the trouble?)

Using scripts (probably the hardest, only recommended if you want the player to interact with the actual battle):
1. event 'Hi, I'm an old man who will catch a weedle'
2. switch the graphics of the player with that of an old man (don't know how to do that, though)
3. enforce an automatic battle (or one with all options disabled except for the one you want to be played). I don't know how to do this either
4. after the battle, switch back the graphics, and delete the pokemon that was just caught. How to delete a Pokemon you can find in the wiki.
5. event 'so that's how the old man caught all his pokemon'.

While it would be entirely possible to make a full-screen frame by frame animation for this, I think that seeing as this is a feature in ALL Pokémon games to date, it's a feature worth adding to essentials. Especially since it could be used for things other than catching tutorials and I think a lot of people would actually use it.

Over in the Rom-Hacking subforums, I have seen a lot of games who utilize the catch tutorial to, for example, show Lance catching Red Gyarados or show Team Rocket catching a legendary Pokémon.

There is great potential in adding the feature is all I'm saying. But it's up to Maruno if he thinks it's worth it.